Select Sauté and add the butter and olive oil to the inner pot and heat until the butter is foaming. Add the mushrooms and cook, stirring occasionally for about 5 minutes. Add the onion and cook for a further 4 minutes, or until soft.
Add the stock, cream, and sherry, and cook until the liquid has reduced by half, about 5 minutes. Stir in the salt and pepper.
Divide the mixture between two ramekins, then break an egg into each of the ramekins, and sprinkle each with the Cheddar cheese.
Rinse out the inner pot and return it to the base. Add 1 cup of water to the inner pot and place the trivet inside. Place the ramekins, uncovered, on the trivet.
Lock the lid into place. Select Pressure Cook High and time to 2 minutes (for runny yolks, 4 minutes for hard yolks) followed by quick release the pressure.
Let the egg cups cool for a minute and top with the chives.